Stability of the Gauss-Huard algorithm with partial pivoting
The paper deals with the stability of a stabilized version of the Gauss-Huard elimination, a variant of the Gaussian elimination, using partial pivoting with column interchanges calculating in floating-point arithmetic and given machine precision when solving dense linear systems. This variant reduces the system to an equivalent diagonal system like Gauss-Jordan elimination, but without requiring more floating-point operations than Gaussian elimination. It is proved that Huard's elimination is as stable as Gauss-Jordan elimination with the appropriate pivoting strategy. Numerical experiments verifying the error analysis are supplied.
scientific article; zbMATH DE number 1043129
scientific article